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The direction vector of milling cutter for CL-data of five-axis milling is obtained by the fact
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that the bottom part of the milling cutter rides on free-form surfaces using the z-map method.
Since the direction vector is known, CL-data can be transformed to the NC-code with regard to
the geometry of the five-axis machine and post-processing. For uniform surfaces, the tool path
i5, created from the prediction of cusp heights. After generating the NC-code, a sculptured surface
was machined by five-axis end milling and cusp heights on the machined surface were measured
by a three-dimensional CMM with laser scanner. From this machining test, it was found that this
machining method is effective.10076
Key Words: Cutter Axis Direction, Cusp Height, Five-Axis Machining, Sculptured Surface,
Tool Path1. Introduction
In three-axis machining of sculptured surface
using a ball-end mill cutter, machinability at the
bottom of the ball end mill cutter is poor. Also
sometimes, workpieces having a complex geome-
try such as an impeller and an inclined hole can
not be machined in three-axis milling. In addition
to that, the ball end mill always produces the cusp
on the machined surface. In order to decrease
cusp heights in the machining of the sculptured
surface with the ball end mill cutter, the tool path
interval must be adjusted in consideration of the
cusp height. Though this method can reduce
polishing time, it requires extensive machining
time. Even if a high speed machining method is
used, since cutting conditions applying low
cutting-force to spindle bearing of a high speed
machine must be selected, cutting time by high
speed machining process is greater than that by a
traditional machining process. Therefore, both
machining time and polishing time can not be
controlled simultaneously at the pn:sent state of
bearing technology. For these reasons, five-axisend milling has been recommended for an effec-
tive machining of the free-form surface (Tonshoff
et ai, 1989; Mason, 1991).
When machining sculptured surfaces on a five-
axis CNC milling machine with the end mill
cutter, the direction vector of the milling cutter
must be determined inevitably (Vickers et ai,
1989). The direction vector of the milling cutter is
obtained by the fact that the bottom plane of the
milling cutter must move along a tool path
without interfering with free-form surfaces. Here,
the z-map method is used for interference check. If
the direction vectors are known, NC-code can be
generated according to the geometry of five-axis
milling machine and post-processing. In the
machining of sculptured surfaces with five-axis
milling machine and end mill cutter, cutter axis
direction vectors become different with positions
of the cutter contact point, and cusp heights are
largdy varied from this vector. For reference
surfaces, tool path must be generated from the
predicted cusp heights. If cusp height is obtained
from the normal height between the surface and
intersection point of two ellipses by the projection
of the bottom plane of the milling cutter, these
predicted cusp heights can be applied only to a
straight tool path (Vickers et ai, 1989). In this
study, the cusp height is predicted from a math-
ematical modeling of cutting traces on the com-
mon plane defined along with the tool path. Since
cusp heights in five-axis end milling are very
small, grinding process may be omitted and only
polishing process may be needed (Tonshoff et ai,
1989). Thus, uniform surfaces are needed for the
redu,~tion of geometric error in this process. Also,
straight tool path may be necessary for work
convenience in the manual polishing process.